We have p,q,r,s,t and u asnonnegative real numbers.
(a) Show that (p^2 + q^2)^2 (r^4 + s^4)(t^4 + u^4) ≥ (prt + qsu)^4.
(b) Show that (p^2 + q^2)(r^2 + s^2)(t^2 + u^2) ≥ (prt + qsu)^2.
i wanna put it in cauchy-schwarz form, but i can't figure out how to put it into the cauchy-scwarz form, can someone help?
3 answers
if you google generalized cauchy-schwartz inequality you will find some helpful discussions.
for me that didn't work. but i did solve part (a), do you have idea what do with part (b)? i have a hint saying to write it as (p^2 + q^2)(r^2 + s^2) ≥ ((prt + qsu)^2)/(t^2 + u^2) but i don't know what to do after that..
oops sorry the hint said to write it as (p^2 + q^2)(r^2 + s^2) ≥ ((prt + qsu)^2)/(t^2 + u^2)
1 answer